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3 ARISTOTLE ON TRUTH Aristotle s theory of truth, which has been the most influential account of the concept of truth from Antiquity onwards, spans several areas of philosophy: philosophy of language, logic, ontology, and epistemology. In this book, the first dedicated to this topic, Paolo Crivelli discusses all the main aspects of Aristotle s views on truth and falsehood. He analyses in detail the main relevant passages, addresses some well-known problems of Aristotelian semantics, and assesses Aristotle s theory from the point of view of modern analytic philosophy. In the process he discusses most of the literature on Aristotle s semantic theory to have appeared in the last two centuries. His book vindicates and clarifies the often repeated claim that Aristotle s is a correspondence theory of truth. It will be of interest to a wide range of readers working in both ancient philosophy and modern philosophy of language. paolo crivelli is Fellow and Tutor in Classical Philosophy at New College, Oxford. He has published articles on Plato s logic and epistemology, Aristotle s philosophical logic, and Stoic logic.

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5 ARISTOTLE ON TRUTH PAOLO CRIVELLI University of Oxford

6 cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York Information on this title: Paolo Crivelli 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 isbn ebook (EBL) isbn ebook (EBL) isbn hardback isbn hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

7 To the memory of my father Renzo Crivelli and to my mother Katherine Lester Crivelli

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9 Contents Acknowledgements Notes on the text List of abbreviations of titles of Aristotle s works page ix x xi Introduction 1 1 An overview of Aristotle s theory of truth 1 2 Methodology 39 part i bearers of truth or falsehood 1 States of affairs, thoughts, and sentences 45 1 States of affairs 46 2 Thoughts 62 3 Sentences 72 2 Truth conditions for predicative assertions 77 1 Universals 78 2 Truth and falsehood in de Interpretatione Affirmative and negative predicative assertions 86 4 Assertions about individuals vs assertions about universals 89 5 Truth and the categories 95 3 Truth conditions for existential assertions 99 1 Existential assertions concerning simple items Non-composite substances Singular existential assertions concerning material substances 121 part ii empty terms 4 Truth as correspondence A correspondence theory of truth? The Liar 139 vii

10 viii Contents 5 Vacuous terms and empty terms Vacuous subjects or predicates Empty subjects or predicates One assertion vs many assertions 163 part iii truth and time 6 Truth and change Different truth-values at different times Truth and relatives How far is truth from change? Truth and Determinism in de Interpretatione The modal attributes and theses involved in Int Close textual analysis of Int Alternative interpretations 226 Appendix 1 Metaph. 10, 1051 b 1: the text 234 Appendix 2 Metaph. 10, 1051 b 2 3: the text 238 Appendix 3 Int. 7, 17 b 16 18: the text 239 Appendix 4 Appendix 5 Appendix 6 The two-place relations in Aristotle s definition of truth 254 Aristotle s theory of truth for predicative assertions: formal presentation 258 The failure of Bivalence for future-tense assertions: formal presentation 266 References 284 Index of names 313 Index of subjects 319 Index of passages 321

11 Acknowledgements Many friends and colleagues helped me to shape my views on many of the issues addressed by this study, and alerted me to points where improvement was desirable. Early drafts of parts of the book were presented in Cambridge, Clark, Edinburgh, Florence, Liverpool, Oxford, and Pisa. Among the individuals who in various ways helped me to bring this project to completion, I should like to mention Francesco Ademollo, Francesco Adorno, Fabrizio Amerini, Sylvia Berryman, Susanne Bobzien, Ettore Casari, Walter Cavini, David Charles, Francesco Del Punta, Paolo Fait, Michael Frede, Gabriele Galluzzo, Richard Gaskin, Katerina Ierodiakonou, Fred Miller, Peter Milne, Ben Morison, Massimo Mugnai, David Robinson, Gonzalo Rodriguez-Pereyra, Theodore Scaltsas, Annamaria Schiaparelli, David Sedley, Bob Sharples, Robin Smith, Christopher Strachan, John Thorp, Tim Williamson, and an anonymous referee for Cambridge University Press. The responsibility for the remaining shortcomings is of course mine alone. ix

12 Notes on the text LSJ abbreviates the Liddell, Scott, Jones Greek English lexicon. Irefer to Aristotelian passages by the line numbers as they are printed in Bekker s original edition: these in some cases differ from the Bekker lines of widespread editions (e.g., 101 b 38 of Ross s edition of the Topics is 101 b 39 of Bekker s original edition). Similarly, I follow Bekker s numbering of the chapters within each book of the Nicomachean Ethics. For Greek authors I use LSJ s standard abbreviations. For authors other than Aristotle, I normally use the critical editions on which LSJ relies. For Latin authors, I employ abbreviations which are easy to decode and I use standard critical editions. Cf. at the beginning of a footnote indicates that the passages subsequently referred to express views close to those formulated in the portion of the main text to which the footnote pertains. If I disagree with an author, I say so explicitly (I never use cf. to refer to one or more passages that formulate views with which I disagree). I use quotation marks for three purposes: (i) to mention linguistic expressions, e.g. the word dog is a noun; (ii) to indicate that a certain linguistic expression is being used in some special or unusual sense, e.g. Homer is a philosopher ; (iii) to quote a portion of text from some author, e.g. Aristotle says that sentences are true in the same way as the objects (Int. 9, 19 a 33). I use double quotation marks ( and ) only when what would otherwise be occurrences of single quotation marks would be embedded within single quotation marks. x

13 Abbreviations of titles of Aristotle s works APo. APr. Cael. Cat. de An. Div. Somn. EE EN GA GC HA Insomn. Int. Long. MM Mem. Metaph. PA Ph. Po. Pol. Pr. Rh. SE Sens. Somn. Vig. Top. Xen. Posterior Analytics Prior Analytics de Caelo Categories de Anima de Divinatione per Somnia Eudemian Ethics Nicomachean Ethics de Generatione Animalium de Generatione et Corruptione Historia Animalium de Insomniis de Interpretatione de Longaevitate Magna Moralia de Memoria Metaphysics de Partibus Animalium Physics Poetics Politics Problems Rhetoric Sophistici Elenchi de Sensu de Somno et Vigilia Topics de Xenophane xi

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15 Introduction The study of truth is a central part of the philosophical tradition we have inherited from classical Greece. Aristotle played an important role in developing and sharpening the debate in this area and on many issues that are connected with it. I have two primary goals: to offer a precise reconstruction of all of Aristotle s most significant views on truth and falsehood and to gain a philosophical understanding of them. In this introduction I first offer an overview of Aristotle s theory of truth and then discuss the methodology I adopt in pursuing my primary goals. 1 anoverview of aristotle s theory of truth Why an overview? Aristotle speaks about truth and falsehood in passages from several works, mainly the Categories (chapters 4, 5, 10, and 12), de Interpretatione (chapters 1 9), Sophistici Elenchi (chapter 25), de Anima (chapter 3.6), and the Metaphysics (chapters Ɣ 7, 7, 29, E4, and 10). Truth and falsehood are not the main topic of these works: their discussions of truth and falsehood are asides. Reconstructing an Aristotelian theory of truth and falsehood on the basis of such asides poses complicated problems of various sorts. To help readers to keep their orientation through the many bifurcations of the arguments addressing these problems, I decided to offer a concise but precise map of the territory an overview of Aristotle s theory of truth. References to the passages from Aristotle s works that substantiate the attribution of a certain view to him, and an examination of the relevant secondary literature, will be found in the chapters that follow this introduction. Universals. To expound Aristotle s theory of truth, I need to present some of his views on universals and signification. I begin with universals. Luckily, it is not necessary to embark on the daunting task of a complete exposition of Aristotle s views on universals. Aristotle is to this extent 1

16 2 Introduction a realist about universals: in his view, universals are objects whose nature is neither mental nor linguistic (they are neither concepts nor linguistic expressions). He believes that every universal exists when and only when 1 it holds of some individual or other that at some time or other exists. 2 Let me spend a few words explaining why the phrase at some time or other is needed. According to Aristotle, some universals sometimes hold of individuals that do not exist then, but exist at other times. For example, Aristotle seems to think that at any time the universal poet 3 holds of all and only those individual human beings (including those who at that time do not exist) who by that time have authored some poem. In particular, Aristotle would probably grant that although Homer does not exist now, the universal poet holds now of Homer. It is because of universals of this sort that the phrase at some time or other is needed. Aristotle is likely to believe that every universal is everlasting, i.e. exists always. Hence he is likely to be committed to the view that every universal at all times holds of some individual or other that at some time or other exists in short, that all universals are always instantiated. This of course leaves the possibility open that every individual that at some time or other exists and of which a certain universal holds at one time could be other than every individual that at some time or other exists and of which the same universal holds at a certain other time in short, the possibility remains that some universal could be instantiated by different individuals at different times. Signification.I now move on to expound some of Aristotle s views on signification. Aristotle thinks that some utterances of certain noun-phrases and certain adjectival phrases signify a single universal: e.g. he would grant that some utterances of man signify the universal man and that some utterances of white signify the universal white. He also thinks that some utterances of certain noun-phrases signify a single individual: e.g. he would grant that some utterances of Socrates signify Socrates, the Athenian philosopher executed in 399 bc. However, he believes that some utterances of certain 1 I use when and only when in a strictly temporal sense, i.e. as equivalent to at all and only the times at which. 2 I use to hold of to express the relation of a universal to its instances. Following Aristotle s lead, I sometimes use to be predicated of to express this same relation. 3 I normally refer to a universal by simply using a linguistic expression that signifies it (if this linguistic expression is a phrase, I hyphenate it); I avoid referring to a universal by italicising, or enclosing in quotation marks, a linguistic expression that signifies it. For example, I normally refer to universals by means of expressions like the universal poet or the universal man-who-authored-a-poem ; I avoid referring to universals by means of expressions like the universal poet or the universal poet.

17 Introduction 3 noun-phrases and some of certain adjectival phrases signify neither a single universal nor a single individual: e.g. he would concede that some utterances of walking white man or walking, white, and tall signify neither a single universal nor a single individual (he would claim that each of these utterances signifies many universals which do not coalesce in a single universal). What can be true or false? Having presented Aristotle s views on universals and signification that are necessary to understand his theory of truth, I am in a position to begin addressing the main themes of the latter. Let me start with Aristotle s conception of the bearers of truth or falsehood. According to Aristotle, items that are true or false are of three main kinds: sentences, thoughts, and certain objects whose nature is neither mental nor linguistic. The sentences that are true or false are sentencetokens, utterances, events of speech that occur over relatively short portions of time. Similarly, the thoughts that are true or false are thought-tokens, either mental events that occur over relatively short portions of time or thinker-individuated mental states. For Aristotle, events of perceiving and imagining also are true or false. Events of perceiving and imagining fall under none of the three kinds I just mentioned: they are neither thoughts, nor sentences, nor objects whose nature is neither mental nor linguistic. Since Aristotle s views on the truth and falsehood of events of perceiving and imagining are somewhat isolated from the rest of his reflection on truth and falsehood, in this introduction I shall say nothing more about them. A puzzling view.a particularly puzzling part of Aristotle s theory of truth is his view that among items that are true or false there are objects (I sometimes use object to mean object whose nature is neither mental nor linguistic : Itrust that the context will make it clear whether a given occurrence of object is to be understood in this narrow sense). On this point Aristotle s theory of truth is radically different from some modern ones: modern philosophers are ready to acknowledge that certain thoughts or sentences are true or false, but some of them would jib at the suggestion that some objects are true or false. These objects that are true or false occupy a central position in Aristotle s theory of truth. What are they? What roles do they play in Aristotle s theory of truth? What are the objects that are true or false? Aristotle distinguishes two kinds of objects that are true or false: composite objects and simple objects.

18 4 Introduction Some composite objects that are true or false are states of affairs. 4 A state of affairs, which is an object, is composed of two further objects: one of the objects of which it is composed is a universal, the other is either a universal or an individual. A state of affairs is true when and only when the objects of which it is composed are reciprocally combined in the relevant way; it is false when and only when the objects of which it is composed are reciprocally divided in the relevant way. 5 For example, the state of affairs that Socrates is seated is composed of the universal seated and of the individual Socrates; it is true when and only when the universal seated is combined in the relevant way with Socrates, i.e. when and only when Socrates is seated; it is false when and only when the universal seated is divided in the relevant way from Socrates, i.e. when and only when Socrates is not seated. Again, the state of affairs that every diagonal is commensurable is composed of the universal commensurable and of the universal diagonal; it is true when and only when the universal commensurable is combined in the relevant way with the universal diagonal, i.e. when and only when every diagonal is commensurable; it is false when and only when the universal commensurable is divided in the relevant way from the universal diagonal, i.e. when and only when some diagonal is not commensurable. Since no diagonal ever is commensurable, the state of affairs that the diagonal is commensurable is never true but always false. Aristotle allows only affirmative states of affairs: among states of affairs there are the state of affairs that Socrates is seated and the state of affairs that every diagonal is commensurable, but there is not a state of affairs that Socrates is not seated nor is there one that not every diagonal is commensurable. In principle, a state of affairs can exist at a time when it is false, i.e. at a time when the objects of which it is composed are reciprocally divided in the relevant way. For example, the state of affairs that Socrates is seated exists at certain times when it is false; again, the state of affairs that every diagonal is commensurable always exists and is always false. The combination that makes a state of affairs true is not to be confused with the composition whereby the state of affairs is composed of further objects. By the same token, the division that makes a state of affairs false does not destroy the composition whereby the state of affairs is composed of further objects (otherwise the state of affairs could not, even in principle, exist at any time when it is false). For example, the state of 4 State of affairs can be used in several senses. I use it to denote objects of a propositional nature of which it is sensible to say both that they obtain and that they do not obtain at a time. 5 To becombined and to be divided are technical expressions. I hope that the examples in this paragraph s sequel will provide an intuitive grasp of their meaning. They will be discussed in greater detail later in this introduction.

19 Introduction 5 affairs that Socrates is seated remains composed of the universal seated and of the individual Socrates even when the universal seated is divided from the individual Socrates in such a way as to make the state of affairs in question false. It remains unclear whether in Aristotle s view all states of affairs are everlasting: does Aristotle believe that the state of affairs that Socrates is seated exists both before and after Socrates exists? A state of affairs, as it is conceived of by Aristotle, is best understood as an object corresponding to a complete present-tense affirmative predicative assertion, and as being composed of the objects signified by the assertion s predicate and subject. For example, the state of affairs that Socrates is seated corresponds to the whole present-tense affirmative predicative assertion that is an utterance of Socrates is seated, and is composed of the universal seated, which is signified by the assertion s predicate (an utterance of seated ), and of the individual Socrates, who is signified by the assertion s subject (an utterance of Socrates ). As I said, some composite objects that are true or false are states of affairs. According to Aristotle, material substances (e.g. Socrates and the horse Bucephalus) are composite objects in that they consist of form and matter. Material substances are not states of affairs, but they resemble states of affairs in interesting respects: as for a state of affairs to be true is to be combined, so for a material substance to exist is to be combined, i.e. it is for its form to be combined with its matter; as for a state of affairs to be false is to be divided, so for a material substance not to exist is to be divided, i.e. it is for its form to be divided from its matter. Aristotle perhaps thinks that material substances rank among the composite objects that are true or false, that for a material substance to be true is to exist, and that for a material substance to be false is not to exist. I can use only the cautious expression Aristotle perhaps thinks... because the evidence for attributing the position in question to Aristotle is far less than clear cut. However, independently of whether Aristotle does endorse the position in question, at least two differences between states of affairs and material substances are worth noting. First, while some state of affairs exists at times when it is false, no material substance exists at times when it is false (because, according to the position in question, for a material substance to be false is not to exist). Second, although some material substances (i.e. celestial bodies) are everlasting, most are not; on the other hand, Aristotle does not state how long states of affairs exist, but his position might well be that all states of affairs are everlasting. Since a simple object has no components between which combination or division could obtain, for a simple object to be true cannot be to be

20 6 Introduction combined, nor can for it to be false be to be divided. Rather, for a simple object to be true is simply to exist, and for it to be false is simply not to exist. Aristotle distinguishes two kinds of simple objects: essences and incorporeal substances. Essences are natural kinds (e.g. the kind horse). 6 The remaining simple objects, incorporeal substances, are God and (perhaps) the intellects that move the heavenly spheres. 7 The application of true to incorporeal substances should not arouse wonder: true is one of the epithets traditionally used to speak of God. Both essences and incorporeal substances are everlasting, i.e. exist always. Hence, all simple objects exist always. The sense of true and false whereby they apply to objects is probably Aristotle s own creation: it is an extension of the ordinary sense of these expressions which Aristotle introduces in order to construct a better theory of truth. It is not, however, completely unconnected with ordinary usage: true can be used (both in Greek and in English) to mean real (as in true coin ), and real is connected with existent (although real and existent are used differently, one can employ the phrase the contrast between dreams and what is real to describe the discrepancy between what exists and what someone would like to exist). Aristotle s views on the nature of the bearers of truth or falsehood can now be conveniently summarised by the following schema: bearers of truth or falsehood sentences thoughts objects whose nature is neither mental nor linguistic composite simple states of affairs material substances (?) essences incorporeal substances 6 Aristotle s remarks on essence are difficult to understand and are variously interpreted. The view I am attributing to Aristotle here, i.e. that essences are natural kinds, is minimal in that it is compatible with, and perhaps implied by, several of these interpretations. 7 By material and immaterial I mean containing matter and (respectively) not containing matter. By corporeal and incorporeal I mean either containing or mixed with matter and (respectively) neither containing nor mixed with matter. Thus: Socrates is a material and corporeal substance; Socrates essence is an immaterial but corporeal substance; God is an immaterial and incorporeal substance.

21 Introduction 7 What roles do the objects that are true or false play in Aristotle s theory of truth? Objects that are true or false play three roles in Aristotle s theory of truth: first, they contribute to explaining what it is to be true or false for items of other kinds which can be such, i.e. for thoughts and sentences; second, they are bearers of modal attributes; third, they are targets of propositional attitudes. In the following subsections I shall examine these three roles in turn. The first role of objects that are true or false: contributing to explaining what it is to be true or false for thoughts and sentences. AsIjust said, the first role played in Aristotle s theory of truth by objects that are true or false is to contribute to explaining what it is to be true or false for thoughts and sentences. This role recalls a strategy which is often adopted in modern philosophy of logic, from Frege onwards: that of explaining the truth and falsehood of certain mental states and certain sentences by appealing to the truth and falsehood of propositions (abstract entities whose nature is neither mental nor linguistic). Although there are important differences between Aristotle s conception and the modern strategy, at this stage I would like to call attention to the resemblance. To expound how objects that are true or false contribute to explaining what it is to be true or false for thoughts and sentences, I must say something about Aristotle s views on thoughts and sentences that are true or false. Truth-evaluable sentences. Not every sentence is either true or false: some are neither (e.g. prayers). Every sentence that is true or false is an assertoric sentence, or (as Aristotle often calls it) an assertion. But the converse fails: some assertions are neither true nor false (read on to find out which). Assertions coincide with truth-evaluable sentences, i.e. with the sentences with regard to which the question Is it true or false? can be reasonably asked. Note that this question cannot be reasonably asked with regard to certain sentences (e.g. prayers). In the case of some sentences with regard to which the question Is it true or false? can be reasonably asked, the correct answer is Neither. An analogy helps to clarify. Physical objects coincide with colour-evaluable objects, i.e. with the objects with regard to which the question What colour is it? can be reasonably asked. Note that this question cannot be reasonably asked with regard to certain objects (e.g. numbers). In the case of some objects with regard to which the question What colour is it? can be reasonably asked, the correct answer is None (e.g. some transparent objects like crystal balls or diamonds).

22 8 Introduction Assertions are utterances, i.e. expression-tokens (not expression-types), events of speech that occur over relatively short portions of time. Truth-evaluable thoughts. Aristotle does not explicitly isolate a class of truthevaluable thoughts that constitute the mental counterparts of assertions. However, since he regards the spheres of thought and speech as closely analogous, indeed, almost as isomorphic, he is likely to believe that there is such a class of truth-evaluable thoughts corresponding to the class of truth-evaluable sentences, i.e. to the class of assertions. Some of Aristotle s remarks indicate that he would agree that every belief is a truth-evaluable thought, i.e. a thought with regard to which the question Is it true or false? can be reasonably asked. However, I doubt that Aristotle would claim that every truth-evaluable thought is a belief. Hence, for Aristotle beliefs probably constitute a proper subclass of truth-evaluable thoughts. I guess Aristotle would grant that not every belief is either true or false. Simple and composite assertions. Aristotle distinguishes two kinds of assertions: simple assertions and composite assertions. An assertion is simple just in case it concerns exactly one object; it is composite just in case it concerns more than one object. Every simple assertion is either affirmative or negative. Composite assertions are equivalent to utterances constructed from several assertions linked by connective particles. Aristotle concentrates on simple assertions, i.e. assertions that concern exactly one object. He has little to say about composite assertions: he acknowledges their existence, but they remain at the margins of his reflection. He never states that some sentences that are true or false have no assertoric force (like the utterance of Socrates is seated which is a part of an utterance of Either Socrates is seated or Socrates is not seated ). Nor does he discuss utterances of Either Socrates is seated or Socrates is seated : are they simple (because they concern exactly one object, i.e. the state of affairs that Socrates is seated) or composite (because they are disjunctive)? Simple beliefs. Aristotle does not explicitly isolate a class of simple beliefs that are the mental counterparts of simple assertions. However, since (as I said) he regards the spheres of thought and speech as closely analogous, he is likely to take such a class for granted: he probably thinks that simple beliefs are those beliefs that concern exactly one object, and that every simple belief is either affirmative or negative.

23 Introduction 9 A general definition of truth and falsehood for simple beliefs and assertions. Having expounded Aristotle s views on thoughts and sentences that are true or false, I am now in a position to address his conception of how objects that are true or false contribute to explaining what it is to be true or false for thoughts and sentences. Objects play this role, in particular, with regard to simple beliefs and simple assertions. Aristotle s theory of truth and falsehood for simple beliefs and assertions is governed by a general definition of truth and falsehood (henceforth DTF ): DTF Every simple belief, or assertion, concerns exactly one object and is either affirmative or negative. Every affirmative simple belief, or assertion, posits that the object it concerns is true. Accordingly, an affirmative simple belief, or assertion, is true when and only when the object it concerns is true; an affirmative simple belief, or assertion, is false when and only when the object it concerns is false. Every negative simple belief, or assertion, posits that the object it concerns is false. Accordingly, a negative simple belief, or assertion, is true when and only when the object it concerns is false; a negative simple belief, or assertion, is false when and only when the object it concerns is true. DTF is a definition of truth (at least for simple beliefs and assertions). Aristotle does not address the issue of the criterion of truth (roughly, the issue of establishing what, if any, reliable ways humans have of discovering truths). Aristotle s silence on the issue of the criterion of truth is remarkable in view of the fact that shortly after his death, with the advent of the Hellenistic philosophical schools of the third and second centuries bc, this issue becomes a hot topic of philosophical debate. DTF covers at one blow all simple beliefs and assertions, those concerning composite objects as well as those concerning simple ones. It is worthwhile working out the details of Aristotle s account for each case. So, let us examine the forms taken on by DTF with simple beliefs and assertions concerning composite objects and with simple beliefs and assertions concerning simple objects. However, there are two kinds of composite objects: states of affairs and material substances. Let us then study the forms of DTF with regard to simple beliefs and assertions concerning (i) those composite objects that are states of affairs, (ii) those composite objects that are material substances, and (iii) simple objects.

24 10 Introduction Predicative assertions and beliefs. The simple assertions which concern those composite objects that are states of affairs are predicative assertions; similarly, the simple beliefs that concern those composite objects that are states of affairs are predicative beliefs. Let me first spend a few paragraphs explaining Aristotle s views on predicative assertions and predicative beliefs. Predicative assertions display a subject predicate structure (this can be clearly seen in examples of predicative assertions like utterances of the sentence-type Socrates is seated or of the sentence-type Socrates is not seated ). Every predicative assertion has at least three parts: the predicate, the subject, and the copula. In every predicative assertion, the predicate signifies a universal, the subject signifies either a universal or an individual, and the copula combines with the predicate to form a predicative expression. Consider a predicative assertion that is an utterance of Socrates is seated : the predicate is the part of the assertion that is an utterance of the adjective seated and signifies the universal seated; the subject is the part of the assertion that is an utterance of the name Socrates and signifies the individual Socrates; and the copula is the part of the assertion that is an utterance of is and combines with the predicate to form the predicative expression that is an utterance of is seated. Every predicative assertion is either affirmative (e.g. an utterance of Socrates is seated ) or negative (e.g. an utterance of Socrates is not seated ). Many predicative assertions have further parts over and above the predicate, the subject, and the copula: they contain utterances either of a negative particle (an utterance of not, as in an utterance of Socrates is not seated ) or of a quantifying expression (an utterance of every, no, some, or not every, as in an utterance of No horse is white ). Many assertions that contain no copula are regarded by Aristotle as equivalent to assertions that do contain one: e.g. for Aristotle an utterance of Socrates walks is equivalent to one of Socrates is walking. Note that in English Socrates is walking is not equivalent to Socrates walks. Aristotle s view, however, is correct with respect to Greek usage: the Greek sentence-type rendered by Socrates is walking is in fact equivalent to that rendered by Socrates walks. A predicative belief is a belief whose literal linguistic expression would be a predicative assertion. For example, Plato s belief that Socrates is seated is a predicative belief because its literal linguistic expression would be a predicative assertion that is an utterance of Socrates is seated. Every predicative belief has a part that constitutes its predicate (it is about, or concerns, or as I shall often say grasps a universal) and one that constitutes its subject (it grasps either a universal or an individual). For example, in Plato s belief that Socrates is seated, the predicate is the part

25 Introduction 11 of the belief that grasps the universal seated, the subject is the part that grasps the individual Socrates. Every predicative belief is either affirmative (e.g. Plato s belief that Socrates is seated) or negative (e.g. Simmias belief that Socrates is not seated). Note that the predicate and the subject of a predicative assertion are utterances, and they signify objects; the predicate and the subject of a predicative belief are thoughts, and they grasp objects. Aristotle s classification of predicative beliefs and assertions. Aristotle has a richly articulated classification of predicative beliefs and assertions. Predicative beliefs and assertions divide into two main groups: singular and general predicative beliefs and assertions. A predicative belief, or assertion, is singular just in case its subject grasps, or signifies, an individual; it is general just in case its subject grasps, or signifies, a universal. Examples of singular predicative assertions are utterances of Socrates is seated and Socrates is not seated. As for general predicative beliefs and assertions, they divide into two subordinate groups: indeterminate and quantified predicative beliefs and assertions. Examples of indeterminate predicative assertions are utterances of A horse is white and A horse is not white. As for quantified predicative beliefs and assertions, they divide into two subordinate groups: particular and universal predicative beliefs and assertions. Examples of particular predicative assertions are utterances of Some horse is white and Not every horse is white ; examples of universal predicative assertions are utterances of Every horse is white and No horse is white. Aristotle s classification of predicative beliefs and assertions is conveniently summarised by the following schema: predicative beliefs and assertions singular general indeterminate quantified particular universal The distinction between affirmative and negative predicative beliefs and assertions cuts across the above classification: every group within this

26 12 Introduction classification is divided into an affirmative and a negative subordinate group. That is, universal predicative beliefs and assertions divide into universal affirmative and universal negative predicative beliefs and assertions; particular predicative beliefs and assertions divide into particular affirmative and particular negative predicative beliefs and assertions; similarly with indeterminate and singular predicative beliefs and assertions. Aristotle has little to say about indeterminate predicative beliefs and assertions. Following his lead, I shall concentrate on universal, particular, and singular predicative beliefs and assertions. The relationship of predicative beliefs and assertions to states of affairs.having explained Aristotle s conception of predicative beliefs and assertions, I am now in a position to report his views on how predicative beliefs and assertions are related to states of affairs. Every predicative belief, or assertion, concerns exactly one state of affairs whose two components are, first, the universal grasped, or signified, by the predicate of the predicative belief, or assertion, and, second, the object (a universal or an individual) grasped, or signified, by the subject of the predicative belief, or assertion. For example, a predicative assertion that is an utterance of Socrates is seated concerns the state of affairs that Socrates is seated, which is composed of the universal seated (signified by the assertion s predicate, an utterance of seated ) and the individual Socrates (signified by the assertion s subject, an utterance of Socrates ). Note that a predicative assertion that is an utterance of Socrates is not seated concerns the same state of affairs: the state of affairs that Socrates is seated. Again, a predicative assertion that is an utterance of Every diagonal is commensurable concerns the state of affairs that every diagonal is commensurable, which is composed of the universal commensurable (signified by the assertion s predicate, an utterance of commensurable ) and the universal diagonal (signified by the assertion s subject, an utterance of diagonal ). Note that a predicative assertion that is an utterance of Not every diagonal is commensurable concerns the same state of affairs: the state of affairs that every diagonal is commensurable. DTF and predications.in the case of predicative beliefs and assertions, DTF takes on the following form: an affirmative predicative belief, or assertion, is true when and only when the state of affairs it concerns is true, i.e. when and only when the components of this state of affairs are reciprocally combined in the relevant way, i.e. when and only when the universal grasped, or signified, by the predicate is combined in the relevant way with the object

27 Introduction 13 (a universal or an individual) grasped, or signified, by the subject. An affirmative predicative belief, or assertion, is false when and only when the state of affairs it concerns is false, i.e. when and only when the components of this state of affairs are reciprocally divided in the relevant way, i.e. when and only when the universal grasped, or signified, by the predicate is divided in the relevant way from the object grasped, or signified, by the subject. A negative predicative belief, or assertion, is true when and only when the state of affairs it concerns is false, i.e. when and only when the components of this state of affairs are reciprocally divided in the relevant way, i.e. when and only when the universal grasped, or signified, by the predicate is divided in the relevant way from the object grasped, or signified, by the subject. A negative predicative belief, or assertion, is false when and only when the state of affairs it concerns is true, i.e. when and only when the components of this state of affairs are reciprocally combined in the relevant way, i.e. when and only when the universal grasped, or signified, by the predicate is combined in the relevant way with the object grasped, or signified, by the subject. Truth conditions for predications that differ in quantity. Different relations of combination and division are associated with predicative beliefs and assertions that differ in quantity (i.e. by being universal, particular, or singular). I shall first offer an abstract exposition of how different relations of combination and division are called for in an account of true and false predicative beliefs and assertions that differ in quantity ; afterwards I shall offer some examples. Here is the abstract exposition: [a] Every universal affirmative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as universally to hold of it. Accordingly, a universal affirmative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as universally to hold of it. A universal affirmative predicative belief, or assertion, is false when and only when the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as not universally to hold of it. [b] Every universal negative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as universally to

28 14 Introduction fail to hold of it. Accordingly, a universal negative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as universally to fail to hold of it. A universal negative predicative belief, or assertion, is false when and only when the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as not universally to fail to hold of it. [c] Every particular affirmative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as not universally to fail to hold of it. Accordingly, a particular affirmative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as not universally to fail to hold of it. A particular affirmative predicative belief, or assertion, is false when and only when the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as universally to fail to hold of it. [d] Every particular negative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as not universally to hold of it. Accordingly, a particular negative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is divided from the universal grasped, or signified, by its subject in such a way as not universally to hold of it. A particular negative predicative belief, or assertion, is false when and only when the universal grasped, or signified, by its predicate is combined with the universal grasped, or signified, by its subject in such a way as universally to hold of it. [e] Every singular affirmative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is combined with the individual grasped, or signified, by its subject in such a way as to hold of it. Accordingly, a singular affirmative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is combined with the individual grasped, or signified, by its subject in such a way as to hold of it. A singular affirmative predicative belief, or assertion, is false when and only when the universal grasped,

29 Introduction 15 or signified, by its predicate is divided from the individual grasped, or signified, by its subject in such a way as to hold outside it. [f ] Every singular negative predicative belief, or assertion, posits that the universal grasped, or signified, by its predicate is divided from the individual grasped, or signified, by its subject in such a way as to hold outside it. Accordingly, a singular negative predicative belief, or assertion, is true when and only when the universal grasped, or signified, by its predicate is divided from the individual grasped, or signified, by its subject in such a way as to hold outside it. A singular negative predicative belief, or assertion, is false when and only when the universal grasped, or signified, by its predicate is combined with the individual grasped, or signified, by its subject in such a way as to hold of it. To pin down the above, a definition of the relevant relations of combination and division is called for. A universal u is combined with a universal v in such a way as universally to hold of it when and only when u holds of every individual of which v holds. A universal u is divided from a universal v in such a way as universally to fail to hold of it when and only when every individual of which v holds is other than every individual of which u holds. A universal u is combined with a universal v in such a way as not universally to fail to hold of it when and only when u holds of at least one individual of which v holds. A universal u is divided from a universal v in such a way as not universally to hold of it when and only when at least one individual of which v holds is other than every individual of which u holds. A universal u is combined with an individual i in such a way as to hold of it when and only when u holds of i. Auniversal u is divided from an individual i in such a way as to hold outside it when and only when i is other than every individual of which u holds. Some examples will clarify the abstract exposition of the previous subsection. A universal affirmative predicative assertion that is an utterance of Every horse is white posits that the universal white, signified by the predicate (an utterance of white ), is combined with the universal horse, signified by the subject (an utterance of horse ), in such a way as universally to hold of it. Accordingly, this utterance is true when and only when the universal white is combined with the universal horse in such a way as universally to hold of it, i.e. when and only when the universal white holds of every individual of which the universal horse holds; the same utterance is false when and only when the universal white is divided from the universal horse in such a way as not universally to hold of it, i.e. when and only when at least one

30 16 Introduction individual of which the universal horse holds is other than every individual of which the universal white holds. Hence, now the utterance of Every horse is white is not true (for it is not the case that the universal white now holds of every individual of which the universal horse now holds), but false (for at least one individual of which the universal horse now holds is other than every individual of which the universal white now holds). Again, a universal negative predicative assertion that is an utterance of No horse is white posits that the universal white, signified by the predicate (an utterance of white ), is divided from the universal horse, signified by the subject (an utterance of horse ), in such a way as universally to fail to hold of it. Accordingly, this utterance is true when and only when the universal white is divided from the universal horse in such a way as universally to fail to hold of it, i.e. when and only when every individual of which the universal horse holds is other than every individual of which the universal white holds; the same utterance is false when and only when the universal white is combined with the universal horse in such a way as not universally to fail to hold of it, i.e. when and only when the universal white holds of at least one individual of which the universal horse holds. Hence, now the utterance of No horse is white is not true (for it is not the case that every individual of which the universal horse now holds is other than every individual of which the universal white now holds), but false (for the universal white now holds of at least one individual of which the universal horse now holds). Predications that differ in category. Different relations of combination and division are associated (not only with predicative beliefs and assertions that differ in quantity, but also) with predicative beliefs and assertions that differ in category. There are several versions (or, perhaps, aspects) of Aristotle s theory of the categories. In one of these versions, the categories are predicative relations linking objects. Different categories correspond to different fundamental questions: the category of substance is the predicative relation linking a kind to its subordinate kinds and to its members, and corresponds to the question What is it? ; the category of quality is the predicative relation linking a quality to the items it holds of, and corresponds to the question What is it like? ; etc. 8 Moreover, there are predicative relations 8 The question What is it? can be used in a wide range of ways. Within this range we can pick out a sharp question which is truly and appropriately answered by mentioning the kind under which the object referred to by it falls. If someone pointing to Socrates (who, as it happens, is pale) asks What is it?, It is a man and It is an animal are true and appropriate answers (they mention the